Reasoning, convincing and proving

problem
Three neighbours

Age

7 to 14

Challenge level

Take three consecutive numbers and add them together. What do you notice?
problem
Euler meets Schlegel

Age

16 to 18

Challenge level

Discover how networks can be used to prove Euler's Polyhedron formula.
problem
Network trees

Age

14 to 18

Challenge level

Explore some of the different types of network, and prove a result about network trees.
article
An introduction to number theory

An introduction to some beautiful results in Number Theory.
problem
Always perfect

Age

14 to 18

Challenge level

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
problem
Common divisor

Age

14 to 18

Challenge level

Can you find out what numbers divide these expressions? Can you prove that they are always divisors?
problem
Equivalent pairs

Age

5 to 7

Challenge level

Can you match pairs of cards which show the same amount?
interactivity
Interactive balance

Age

5 to 11

Challenge level

In this simulation of a balance, you can drag numbers and parts of number sentences on to the trays. Have a play!
problem
True or false?

Age

7 to 11

Challenge level

Without doing lots of calculations, can you decide which of these number sentences are true? How do you know?
problem
Sweetie box

Age

5 to 11

Challenge level

Max and Bryony both have a box of sweets. What do you know about the number of sweets they each have?